Question 13
We place, forming a circle, 2004 two-color chips: white on one side and black on the other. A move consists of choosing a piece with the black side facing up and turning over three pieces: the chosen one, the one on its right, and the one on its left. Suppose there is initially a single token with the black side facing up. Will it be possible, by repeating the movement described, to ensure that all the pieces have the white side facing up? What if we had 2003 tiles, among which exactly one has the black side facing up at the beginning?